Find a or b

Free interactive math game: Find a or b — y = ax + b through points. Part of the Analytic Geometry category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. y = ax + b passes through (-3, -5) and (3, 13). Find b:
  2. y = ax + b passes through (4, -4) and (-1, 6). Find b:
  3. y = ax + b passes through (1, 2) and (-3, -6). Find b:
  4. y = ax + b passes through (-4, -10) and (0, -2). Find b:

About this exercise

Finding a coefficient of the line y = ax + b from two points it passes through.

How to solve it

The coefficient a is the change in y divided by the change in x. Substituting one point back then gives b.

Worked example

Through (0, -5) and (2, 1) the rise is 6 over a run of 2, so a = 3.

Common mistake

Dividing the run by the rise. The vertical change always goes on top.